Respostas dos Problemas Halliday ed. 9

M AT E R I A L S U P L E M E N TA R PA R A A C O M PA N H A R
MATERIAL SUPLEMENTAR PARA ACOMPANHAR
FUNDAMENTOS DE FÍSICA
Mecânica
9a Edição
HALLIDAY & RESNICK
JEARL WALKER
Cleveland State University
VOLUME 1
Tradução e Revisão Técnica
Ronaldo Sérgio de Biasi, Ph.D.
Professor Titular do Instituto Militar de Engenharia – IME
Este Material Suplementar contém as Respostas dos Problemas – Volume 1 que podem ser usadas como
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SUMÁRIO
Capítulo 1 1
Capítulo 2 1
Capítulo 3 2
Capítulo 4 3
Capítulo 5 5
Capítulo 6 5
Capítulo 7 6
Capítulo 8 7
Capítulo 9 9
Capítulo 10 10
Capítulo 11 11
Respostas dos Problemas
Capítulo 1
1. (a) 4,00  10 km; (b) 5,10  10 km ; (c) 1,08  10 km
2. 0,18 ponto2
3. (a) 109 m; (b) 10–4; (c) 9,1  105 m
4. (a) 1,9 paica; (b) 23 pontos
5. (a) 160 varas; (b) 40 cadeias
6. (a) 8,33  102; 2,08  102; 6,94  103; 3,47  103;
(b) 0,250. 8,33  102. 4,17  102; (c) 0,333. 0,167; (d)
0,500; (e) 14,0 medios; (f) 4,86  102 cahizes;
(g) 3,24  104 cm3
7. 1,1  103 acres-pés
8. (a) 60,8 W; (b) 43,3 Z
9. 1,9  1022 cm3
10. 15°
11. (a) 1,43; (b) 0,864
12. 3,1 m/s
13. (a) 495 s; (b) 141 s; (c) 198 s; (d) –245 s
14. (a) 52,6 min; (b) 4,9%
15. 1,21  1012 s
16. (a) 3,88  108 rotações; (b) 1557,806 448 872 75 s;
(c) 3  1011 s
17. C, D, A, B, E; o critério importante é a constância dos
resultados e não o seu valor
18. 2,1 h
19. 5,2  106 m
20. (a) 2,69  105 cm3; (b) 0,77 ano
21. 9,0  1049 átomos
22. (a) 1,430 m2; (b) 72,84 km
23. (a) 1  103 kg; (b) 158 kg/s
24. 0,260 kg
25. 1,9  105 kg
26. (a) 2  103 m3. 2  104 m3; (b) 2  106 garrafas. 2 
107 garrafas; (c) 2  106 kg. 2  107 kg
27. (a) 1,18  1029 m3; (b) 0,282 nm
28. 1 quilomol
29. 1750 kg
30. (a) 4,21 s; (b) 23,2 g; (c) 2,89  10–2 kg/min; (d) −6,05
 103 kg/min
31. 1,43 kg/min
32. (a) 1,0 m3; (b) 6,0  104 m3
33. (a) 293 alqueires americanos; (b) 3,81  103 alqueires
americanos
4
8
2
12
3
34. 403 L
35. (a) 22 pecks; (b) 5,5 Imperial bushels; (c) 200 L
36. (a) 0,900; 7,50  102; 1,56  103; 8,32  106;
(b) 1,00; 8,33  102; 1,74  103; 9,24  106; (c) 12,0;
1,00; 2,08  102; 1,11  104; (d) 576; 48; 1,00; 5,32 
103; (e) 1,08  105; 9,02  103; 188; 1,00; (f) 1,96 m3
37. 8  102 km
38. (a) 14,5 roods; (b) 1,47  104 m2
39. (a) 18,8 galões; (b) 22,5 galões
40. 6,0  1026 átomos
41. 0,3 cord
42. (a) 3,0  1026 kg; (b) 5  1046 moléculas
43. 3,8 mg/s
44. 1,3  109 kg
45. (a) sim; (b) 8,6 segundos do universo
46. 0,020 km3
47. 0,12 AU/min
48. 10 u
49. (a) 3,88; (b) 7,65; (c) 156 ken3; (d) 1,19  103 m3
50. 5,95 km
51. (a) 3,9 m, 4,8 m; (b) 3,9  103 mm, 4,8  103 mm;
(c) 2,2 m3. 4,2 m3
52.  1  1036
53. (a) 4,9  106 pc; (b) 1,6  105 anos-luz
54. (a) 11,3 m2/L; (b) 1,13  104 m1; (c) 2,17  103
galões por pé quadrado; (d) o número de galões necessários
para cobrir um pé quadrado
Capítulo 2
1. 13 m
2. (a) 1,74 m/s; (b) 2,14 m/s
3. (a) 40 km/h; (b) 40 km/h
4. 48 km/h
5. (a) 0; (b) –2 m; (c) 0; (d) 12 m; (e) 12 m; (f) 7 m/s
6. 5,554 s
7. 60 km
8. (a) 0,50 m/s; (b) 10 s
9. 1,4 m
10. (a) método 1; (b) 5,76  102 %
11. 128 km/h
12. (a) 48,0 m; (b) 2,5 m/s; (c) o sentido do movimento dos
carros
2
RESPOSTAS DOS PROBLEMAS
13. (a) 73 km/h; (b) 68 km/h; (c) 70 km/h; (d) 0
14. 5,9 m
15. (a) –6 m/s; (b) no sentido negativo; (c) 6 m/s;
(d) diminuindo; (e) 2 s; (f) não
16. (a) 0; (b) 4,0 m; (c) −0,82 s; (d) 0,82 s; (f) 20t;
(g) aumenta
17. (a) 28,5 cm/s; (b) 18,0 cm/s; (c) 40,5 cm/s; (d) 28,1 cm/s;
(e) 30,3 cm/s
18. (a) 54 m; (b) 18 m/s; (c) −12 m/s2; (d) 64 m; (e) 4,0 s;
(f) 24 m/s; (g) 2,0 s; (h) –24 m/s2; (i) 18 m/s
19. −20 m/s2
20. (a) 1,2 s; (b) 0; (c) positivo; (d) negativo
21. (a) 1,10 m/s; (b) 6,11 mm/s2; (c) 1,47 m/s; (d) 6,11 mm/s2
22. (a) m/s2; (b) m/s3; (c) 1,0 s; (d) 82 m; (e) –80 m; (f) 0; (g)
–12 m/s; (h) –36 m/s; (i) −72 m/s; (j) –6 m/s2; (k) –18 m/s2;
(l) –30 m/s2; (m) −42 m/s2
23. 1,62  1015 m/s2
24. (a) (2,6  104)g; (b) (1,3  102)g
25. (a) 30 s; (b) 300 m
26. (a) 0,100 m
27. (a) 1,6 m/s; (b) 18 m/s
28. (a) 5,00 s; (b) 61,5 m
29. (a) 10,6 m; (b) 41,5 s
30. (a) 2,5 s
31. (a) 3,1  106 s; (b) 4,6  1013 m
32. 21g
33. (a) 3,56 m/s2; (b) 8,43 m/s
34. (a) −50 km/h; (b) –2,0 m/s2
35. 0,90 m/s2
36. (a) 56,6 s; (b) 31,8 m/s
37. (a) 4,0 m/s2; (b) positivo
38. (a) 32,9 m/s; (b) 49,1 s; (c) 11,7 m/s
39. (a) –2,5 m/s2; (b) 1; (d) 0; (e) 2
40. (a) tanto faz; (b) não há jeito
41. 40 m
42. (a) 15,0 m; (b) 94 km/h
43. (a) 0,994 m/s2
44. (a) 3,70 m/s; (b) 1,74 m/s; (c) 0,154 m
45. (a) 31 m/s; (b) 6,4 s
46. (a) 183 m/s; (b) não
47. (a) 29,4 m; (b) 2,45 s
48. (a) 1,54 s; (b) 27,1 m/s
49. (a) 5,4 s; (b) 41 m/s
50. 9,6 m/s
51. (a) 20 m; (b) 59 m
52. (a) 0,45 s; (b) 38 m/s; (c) 42 m/s
53. 4,0 m/s
54. (a) 12,3 m/s
55. (a) 857 m/s2; (b) para cima
56. 3,0 m/s
57. (a) 1,26  103 m/s2; (b) para cima
58. (a) 3,41 s; (b) 57 m
59. (a) 89 cm; (b) 22 cm
60. 26 m
61. 20,4 m
62. (a) 350 ms; (b) 82 ms
63. 2,34 m
64. (a) 8,0 m/s2; (b) 20 m/s
65. (a) 2,25 m/s; (b) 3,90 m/s
66. (a) 0,13 m; (b) 0,50 m
67. 0,56 m/s
68. 5,0 m/s
69. 100 m
70. 15,6 m/s
71. (a) 2,00 s; (b) 12 cm; (c) −9,00 cm/s2; (d) para a direita;
(e) para a esquerda; (f) 3,46 s
72. (a) 15,7 m/s; (b) 12,5 m; (c) 82,3 m
73. (a) 82 m; (b) 19 m/s
74. 1,3 s
75. (a) 0,74 s; (b) 6,2 m/s2
76. (a) D23/vp; (b) tr  vp/2a  (D12 – d)/vp
77. (a) 3,1 m/s2; (b) 45 m; (c) 13 s
78. não; 0 e 10 m/s
79. 17 m/s
80. (a) 5,0 m/s2; (b) 4,0 s; (c) 6,0 s; (d) 90 m
81. 47 m/s
82. 39 m/s
83. (a) 1,23 cm; (b) por 4; (c) por 9; (d) por 16; (e) por 25
84. (a) 25g; (b) 400 m
85. 25 km/h
86. (a) 18 m/s; (b) 83 m
87. 1,2 h
88. (a) 5,00 m/s; (b) 1,67 m/s2; (c) 7,50 m
89. 4H
90. (a) 15 m; (b) 2,0 m/s; (c) –2,0 m/s2; (d) 3,5 m/s; (e) 0
91. (a) 3,2 s; (b) 1,3 s
92. (a) 60,6 s; (b) 36,3 m/s
93. (a) 8,85 m/s; (b) 1,00 m
94. 34 m
95. (a) 2,0 m/s2; (b) 12 m/s; (c) 45 m
96. (a) 38,1 m; (b) 9,02 m/s; (c) para baixo; (d) 14,5 m/s;
(e) para cima
97. (a) 48,5 m/s; (b) 4,95 s; (c) 34,3 m/s; (d) 3,50 s
98. 1,5 s
99. 22,0 m/s
100. (a) 17 s; (b) 290 m
101. (a) v  (v20  2gh)0,5; (b) t  [(v20  2gh)0,5 – v0]/g;
(c) igual a (a);
(d) t  [(v20  2gh)0,5  v0]/g, maior que (b)
102. 8,4 m
Capítulo 3
1. (a) –2,5 m; (b) −6,9 m
2. (a) 13 m; (b) 7,5 m
3. (a) 47,2 m; (b) 122°
4. (a) 0,349 rad; (b) 0,873 rad; (c) 1,75 rad; (d) 18,9°;
(e) 120°; (f) 441°
5. (a) 156 km; (b) 39,8° a oeste do norte
6. (a) 4,28 m; (b) 11,7 m
7. (a) 6,42 m; (b) não; (c) sim; (d) sim; (e) uma possível
resposta: (4,30 m) î  (3,70 m) ĵ  (3,00 m) k̂; (f) 7,96 m
RESPOSTAS DOS PROBLEMAS
8. (b) 3,2 km; (c) 41° ao sul do oeste
9. (a) (3,0 m) î − (2,0 m) ĵ  (5,0 m) k̂; (b) (5,0 m) î − (4,0 m)
ĵ − (3,0 m) k̂; (c) (−5,0 m) î  (4,0 m) ĵ  (3,0 m) k̂
10. (a) 12 m; (b) –5,8 m; (c) –2,8 m
11. (a) (−9,0 m) î  (10 m) ĵ; (b) 13 m; (c) 132°
12. (a) 81 km; (b) 40° ao norte do leste
13. 4,74 km
14. (a) –80 m; (b) 110 m; (c) 143 m; (d) 168°
15. (a) 1,59 m; (b) 12,1 m; (c) 12,2 m; (d) 82,5°
16. (a) (8,0 m) î  (2,0 m) ĵ; (b) 8,2 m; (c) 14°; (d) (2,0 m)
î − (6,0 m) ĵ; (e) 6,3 m; (f) –72°
17. (a) 38 m; (b) –37,5°; (c) 130 m; (d) 1,2°; (e) 62 m; (f) 130°
18. (a) 26,6 m; (b) –151°
19. (a) 5,39 m; (b) 21,8º à esquerda
20. (a) 5,0 km; (b) 4,3º ao sul do oeste
21. (a) –70,0 cm; (b) 80,0 cm; (c) 141 cm; (d) –172°
22. (a) (1,28 m) î  (6,60 m) ĵ; (b) 6,72 m; (c) 79,0°;
(d) 1,38 rad
23. 3,2
24. 2,2 m
25. 2,6 km
26. (a) (−3,18 m) î  (4,72 m) ĵ; (b) 5,69 m; (c) 124°
27. (a) 8 î  16 ĵ; (b) 2 î  4 ĵ
28. (a) 0,84 m; (b) 79° ao sul do leste
29. (a) 7,5 cm; (b) 90º; (c) 8,6 cm; (d) 48º
30. (a) 5,0 m; (b) –37°; (c) 10 m; (d) 53°; (e) 11 m; (f) 27°;
(g) 11 m; (h) 80°; (i) 11 m; (j) 260°; (k) 180°
31. (a) aî  aĵ a k̂; (b) –aî  aĵ  a k̂; (c) aî – aĵ  a k̂;
(d) –a î – aĵ  a k̂; (e) 54,7°; (f) 30,5a
32. (a) 9,51 m; (b) 14,1 m; (c) 13,4 m; (d) 10,5 m
33. (a) 12; (b) z; (c) 12; (d) −z; (e) 12; (f) z
34. (a) 2,0 k̂; (b) 26; (c) 46; (d) 5,8
35. (a) –18,8 unidades; (b) 26,9 unidades na direção  z
36. 0
37. (a) –21; (b) –9; (c) 5 î − 11 ĵ − 9 k̂;
38. 540
39. 70,5°
40. (a) 2,81 m2; (b) (1,43 m2) î  (4,86 m2) ĵ − (2,48 m2) k̂;
(c) 63,5°
41. 22°
42. (a) 31 k̂; (b) 8,0; (c) 33; (d) 1,6
43. (a) 3,00 m; (b) 0; (c) 3,46 m; (d) 2,00 m; (e) –5,00 m;
(f) 8,66 m; (g) –6,67; (h) 4,33
44. −3,0 î − 3,0 ĵ − 4,0 k̂;
45. (a) –83,4; (b) (1,14  103) k̂; (c) 1,14  103.  não é
definido.   0°; (d) 90,0°; (e) –5,14 î  6,13 ĵ  3,00 k̂;
(f) 8,54.   130°.   69,4°
46. (a) 4,2 m; (b) 50° ao norte do leste; (c) 8,0 m; (d) 24°
ao norte do oeste
47. (a) 140°; (b) 90,0°; (c) 99,1°
48. (a) 57°; (b) 2,2 m; (c) –4,5 m; (d) –2,2 m; (e) 4,5 m
49. (a) 103 km; (b) 60,9° ao norte do oeste
50. (a) x; (b) y; (c) 0; (d) 0; (e) z; (f) –z; (g) d1d2;
(h) d1d2; (i) d1d2/4; (j) z
51. (a) 27,8 m; (b) 13,4 m
3
52. (a) (9,0 m) î  (6,0 m) ĵ − (7,0 m) k̂; (b) 123°; (c) –3,2 m;
(d) 8,2 m
53. (a) 30; (b) 52
54. (a) 0; (b) –16; (c) –9
55. (a) –2,83 m; (b) –2,83 m; (c) 5,00 m; (d) 0; (e) 3,00 m;
(f) 5,20 m; (g) 5,17 m;
(h) 2,37 m; (i) 5,69 m; (j) 25° ao norte do leste; (k) 5,69 m;
(l) 25° ao sul do oeste
56. (a) (10,0 m) î  (1,63 m) ĵ ; (b) 10,2 m; (c) 9,24°
57. 4,1
58. (a) 10 m; (b) norte; (c) 7,5 m; (d) sul
59. (a) (9,19 m) î’  (7,71 m) ĵ ’; (b) (14,0 m) î’  (3,41 m) ĵ’
60. (a) 9 î  12 ĵ; (b) 3 î  4 ĵ
61. (a) 11 î  5,0 ĵ − 7,0 k̂; (b) 120°; (c) –4,9; (d) 7,3
62. (a) 1,8 m; (b) 69° ao norte do leste
63. (a) 3,0 m2; (b) 52 m3; (c) (11 m2) î  (9,0 m2) ĵ  (3,0 m2) k̂;
64. (a) para deslocamentos paralelos; (b) para
deslocamentos antiparalelos; (c) para deslocamentos
perpendiculares
65. (a) (−40 î −20 ĵ  25 k̂) m; (b) 45 m
Capítulo 4
1. (a) 6,2 m
2. (a) (−5,0 m) î  (8,0 m) ĵ; (b) 9,4 m; (c) 122°;
(e) (8,0 m) î − (8,0 m) ĵ; (f) 11 m;
(g) –45°
3. (−2,0 m) î  (6,0 m) ĵ − (10 m) k̂
4. (a) 14 cm; (b) –135°; (c) 20 cm; (d) 90°; (e) 0; (f) 0
5. (a) 7,59 km/h; (b) 22,5° a leste do norte
6. (a) (3,00 m/s) î − (8,00 m/s2)t ĵ ; (b) (3,00 m/s) î − (16,0
m/s) ĵ; (c) 16,3 m/s; (d) –79,4°
7. (−0,70 m/s) î  (1,4 m/s) ĵ − (0,40 m/s) k̂
8. (a) 1,08  103 km; (b) 26,6° a leste do sul; (c) 480 km/h;
(d) 26,6° a leste do sul; (e) 644 km/h
9. (a) 0,83 cm/s; (b) 0°; (c) 0,11 m/s; (d) −63°
10. (a) 3,50 m/s; (b) –0,125 m/s
11. (a) (6,00 m) î − (106 m) ĵ; (b) (19,0 m/s) î − (224 m/s)
ĵ; (c) (24,0 m/s2) î − (336 m/s2) ĵ; (d) –85,2°
12. (a) 56,6 m; (b) 45° ao norte do oeste (noroeste); (c) 1,89
m/s; (d) 45° ao norte do oeste (noroeste); (e) 0,471 m/s2; (f)
45° ao norte do leste (nordeste)
13. (a) (8 m/s2)t ĵ  (1 m/s) k̂; (b) (8 m/s2) ĵ
14. (a) (−1,5 m/s2) î  (0,50 m/s2) k̂; (b) 1,6 m/s2; (c) 162°
15. (a) (−1,50 m/s) ĵ; (b) (4,50 m) î − (2,25 m) ĵ
16. (a) (−18 m/s2) î; (b) 0,75 s; (c) nunca; (d) 2,2 s
17. (32 m/s) î
18. (a) 15,8 m/s; (b) 42,6°
19. (a) (72,0 m) î  (90,7 m) ĵ; (b) 49,5°
20. 60°
21. (a) 18 cm; (b) 1,9 m
22. (a) 0,495 s; (b) 3,07 m/s
23. (a) 3,03 s; (b) 758 m; (c) 29,7 m/s
24. 25,9 cm
25. 43,1 m/s (155 km/h)
26. (a) 16,9 m; (b) 8,21 m; (c) 27,6 m; (d) 7,26 m;
(e) 40,2 m; (f) 0
4
RESPOSTAS DOS PROBLEMAS
27. (a) 10,0 s; (b) 897 m
28. (a) 51,8 m; (b) 27,4 m/s; (c) 67,5 m
29. 78,5°
30. 5,8 m/s
31. 3,35 m
32. (a) 12,0 m; (b) 19,2 m/s; (c) 4,80 m/s; (d) não
33. (a) 202 m/s; (b) 806 m; (c) 161 m/s; (d) –171 m/s
34. (a) 21,4 m/s; (b) 24,9 m/s; (c) 16,3%
35. 4,84 cm
36. (a) sim; (b) 20 cm; (c) não; (d) 86 cm
37. (a) 1,60 m; (b) 6,86 m; (c) 2,86 m
38. (a) 95 m; (b) 31 m
39. (a) 32,3 m; (b) 21,9 m/s; (c) 40,4° para baixo
40. (a) 24,95 m; (b) 25,02 m
41. 56,4º
42. (a) 5,3 m; (b) 7,9 m; (c) 69 m
43. (a) 11 m; (b) 23 m; (c) 17 m/s; (d) 63°
44. (a) 0,205 s; (b) 0,205 s; (c) 20,5 cm; (d) 61,5 cm
45. (a) na rampa; (b) 5,82 m; (c) 31,0°
46. 70,7%
47. (a) sim; (b) 2,56 m
48. (a) 33,7 m; (b) 26,0 m/s; (c) 71,1°
49. (a) 31°; (b) 63°
50. (a) 20 m/s; (b) 36 m/s; (c) 74 m
51. (a) 2,3°; (b) 1,4 m; (c) 18°
52. 14°
53. (a) 75,0 m; (b) 31,9 m/s; (c) 66,9°; (d) 25,5 m
54. 42 m/s
55. no terceiro
56. (a) 7,49 km/s; (b) 8,00 m/s2
57. (a) 7,32 m; (b) para oeste; (c) para o norte
58. (a) 0,94 m; (b) 19 m/s; (c) 2,4 km/s2; (d) 50 ms
59. (a) 12 s; (b) 4,1 m/s2; (c) para baixo; (d) 4,1 m/s2;
(e) para cima
60. (a) 0; (b) 0
61. (a) 1,3  105 m/s; (b) 7,9  105 m/s2; (c) aumentam
62. 4,0 m/s2
63. 2,92 m
64. (a) 4,00 m; (b) 6,00 m
65. (3,00 m/s2) î  (6,00 m/s2) ĵ
66. (a) 8,82 m; (b) 6,00 m
67. 160 m/s2
68. (a) 5,24 m/s2; (b) 3,33 m/s2
69. (a) 13 m/s2; (b) para leste; (c) 13 m/s2; (d) para leste
70. (a) 5 km/h; (b) x; (c) 1 km/h; (d) –x
71. 1,67
72. 130°
73. (a) (80 km/h) î – (60 km/h) ĵ; (b) 0°; (c) não
74. 240 km/h
75. 32 m/s
76. (a) 185 km/h; (b) 22° ao sul do oeste
77. 60°
78. (a) 24,8 m/s; (b) 83,8° ao norte do leste; (c) 0,40 m/s2;
(d) 60,0° ao norte do leste
79. (a) 38 nós; (b) 1,5° a leste do norte; (c) 4,2 h; (d) 1,5° a
oeste do sul
80. (a) 7,2 m/s; (b) 16° a oeste do norte; (c) 29 s (e não 28 s)
81. (a) (−32 km/h) î − (46 km/h) ĵ; (b) [(2,5 km) – (32 km/
h)t] î  [(4,0 km) – (46 km/h)t] ĵ; (c) 0,084 h; (d) 2  102 m
82. (a) 37° a oeste do norte; (b) 62,6 s
83. (a) –30°; (b) 69 min; (c) 80 min; (d) 80 min; (e) 0°;
(f) 60 min
84. (a) 10 m/s; (b) 19,6 m/s; (c) 40 m; (d) 40 m
85. (a) 2,7 km; (b) 76° no sentido horário
86. (a) 1030 m; (b) oeste
87. (a) 44 m; (b) 13 m; (c) 8,9 m
88. 143 km/h
89. (a) 45 m; (b) 22 m/s
90. 23 ft/s
91. (a) 2,6  102 m/s; (b) 45 s; (c) aumentaria
92. (a) 19 m/s; (b) 35 rev/min; (c) 1,7 s
93. (a) 63 km; (b) 18° ao sul do leste; (c) 0,70 km/h; (d) 18°
ao sul do leste; (e) 1,6 km/h; (f) 1,2 km/h; (g) 33° ao norte
do leste
94. (a) A: 10,1 km, 0,556 km;
B: 12,1 km, 1,51 km;
C: 14,3 km, 2,68 km;
D: 16,4 km, 3,99 km;
E: 18,5 km, 5,53 km;
(b) as pedras formam uma cortina que se encurva para cima
e para longe de você
95. (a) 1,5; (b) (36 m, 54 m)
96. (a) 20,3 m/s; (b) 21,7 m/s
97. (a) 62 ms; (b) 4,8  102 m/s
98. (−2,69 m/s) î  (−1,80 m/s) ĵ
99. 2,64 m
100. (−2,1 m/s2) î  (2,8 m/s2) ĵ
101. (a) 2,5 m; (b) 0,82 m; (c) 9,8 m/s2; (d) 9,8 m/s2
102. (a) 6,7  106 m/s; (b) 1,4  10–7 s
103. (a) 6,79 km/h; (b) 6,96°
104. 7,0 m/s
105. (a) 16 m/s; (b) 23°; (c) acima; (d) 27 m/s; (e) 57°;
(f) abaixo
106. (a) (−7,0 m) î  (12 m) ĵ; (b) ao plano xy
107. (a) 4,2 m, 45°; (b) 5,5 m, 68°; (c) 6,0 m, 90°; (d) 4,2
m, 135°; (e) 0,85 m/s, 135°;
(f) 0,94 m/s, 90°; (g) 0,94 m/s, 180°; (h) 0,30 m/s2, 180°;
(i) 0,30 m/s2, 270°
108. (a) 7,3 km; (b) 80 km/h
109. (a) 5,4  10–13 m; (b) diminui
110. 36 s; não
111. (a) 0,034 m/s2; (b) 84 min
112. mais cerca de 1 cm
113. (a) 8,43 m; (b) –129°
114. (a) 0, 0; 2,0 m, 1,4 m; 4,0 m, 2,0 m; 6,0 m, 1,4 m;
8,0 m, 0; (b) 2,0 m/s, 1,1 m/s; 2,0 m/s, 0; 2,0 m/s, −1,1 m/s;
(c) 0, −0,87 m/s2; 0, −1,2 m/s2; 0, −0,87 m/s2
115. (a) 2,00 ns; (b) 2,00 mm; (c) 1,00  107 m/s; (d) 2,00
 106 m/s
116. (a) 76 m; (b) 4,2 s
117. (a) 24 m/s; (b) 65
RESPOSTAS DOS PROBLEMAS
118. 48 s
119. 93° em relação à direção de movimento do carro
Capítulo 5
1. 2,9 m/s2
2. (a) 0; (b) (4,0 m/s2) ĵ; (c) (3,0 m/s2) î
3. (a) 1,88 N; (b) 0,684 N; (c) (1,88 N) î  (0,684 N) ĵ
4. (−2 N) î  (6 N) ĵ
5. (a) (0,86 m/s²) î − (0,16 m/s²) ĵ; (b) 0,88 m/s²; (c) –11°
6. 241 N
7. (a) (−32,0 N) î − (20,8 N) ĵ; (b) 38,2 N; (c) −147°
8. (−34 î − 12 ĵ) N
9. (a) 8,37 N; (b) −133°; (c) −125°
10. (−7,98 N) î
11. 9,0 m/s2
12. 56°
13. (a) 4,0 kg; (b) 1,0 kg; (c) 4,0 kg; (d) 1,0 kg
14. (a) 2,0 N; (b) para baixo
15. (a) 108 N; (b) 108 N; (c) 108 N
16. (a) 0,26; (b) aumenta
17. (a) 42 N; (b) 72 N; (c) 4,9 m/s2
18. 0,22 m/s
19. 1,2  105 N
20. 6,8  103 N
21. (a) −9,80 ĵ m/s2; (b) 2,35 ĵ m/s2; (c) 1,37 s; (d) (−5,56 
10–3 N)ĵ; (e) (1,333  10–3 N) ĵ
22. (a) (285 N) î  (705 N) ĵ; (b) (285 N) î − (115 N) ĵ;
(c) 307 N; (d) –22,0°; (e) 3,67 m/s2; (f) –22,0°
23. (a) 11,7 N; (b) –59,0°
24. (a) 0; (b) (20 N) î; (c) (−20 N) î; (d) (−40 N) î;
(e) (−60 N) î
25. (a) 0,022 m/s2; (b) 8,3  104 km; (c) 1,9  103 m/s
26. 3,1  102 N
27. 1,5 mm
28. (a) 5,5 kN; (b) 2,7 s; (c) 4,0; (d) 2,0
29. (a) 494 N; (b) para cima; (c) 494 N; (d) para baixo
30. 2,1  102 N
31. (a) 1,18 m; (b) 0,674 s; (c) 3,50 m/s
32. (a) (1,70 N) î  (3,06 N) ĵ; (b) (1,70 N) î  (3,06 N) ĵ;
(c) (2,02 N) î  (2,71 N) ĵ
33. 1,8  104 N
34. (a) 566 N; (b) 1,13 kN
35. (a) 46,7°; (b) 28,0°
36. (a) 68 N; (b) 73 N
37. (a) 0,62 m/s2; (b) 0,13 m/s2; (c) 2,6 m
38. (a) 68 N; (b) 28 N; (c) −12 N
39. (a) 2,2  10–3 N; (b) 3,7  10–3 N
40. 47,4 N
41. (a) 1,4 m/s2; (b) 4,1 m/s
42. (a) 6,8 kN; (b) 201°
43. (a) 1,23 N; (b) 2,46 N; (c) 3,69 N; (d) 4,92 N; (e) 6,15 N;
(f) 0,250 N
44. (a) 7,3 kg; (b) 89 N
45. (a) 31,3 kN; (b) 24,3 kN
46. 16,0 kN
47. 6,4  103 N
5
48. 176 N
49. (a) 2,18 m/s2 ; (b) 116 N; (c) 21,0 m/s2
50. (a) 36,8 N; (b) 19,1 cm
51. (a) 3,6 m/s2; (b) 17 N
52. 5,1 m/s
53. (a) 0,970 m/s2; (b) 11,6 N; (c) 34,9 N
54. 23 kg
55. (a) 1,1 N
56. (a) 2,50 m/s2; (b) 30,0 N
57. (a) 0,735 m/s2; (b) para baixo; (c) 20,8 N
58. (a) 466 N; (b) 527 N; (c) 931 N; (d) 1,05 kN; (e) 931 N;
(f) 1,05 kN; (g) 1,86 kN; (h) 2,11 kN
59. (a) 4,9 m/s2; (b) 2,0 m/s2; (c) para cima; (d) 120 N
60. (a) –5,90  10–4 m/s3; (b) 5,90  10–4 m/s3
61. 2Ma/(a  g)
62. (a) 12,76 m/s; (b) 12,54 m/s; (c) 1,69%
63. (a) 8,0 m/s; (b)  x
64. (a) 3,1 N; (b) 15 N
65. (a) 0,653 m/s3; (b) 0,896 m/s3; (c) 6,50 s
66. 18 kN
67. 81,7 N
68. 334,8 N
69. 2,4 N
70. (a) 245 m/s2; (b) 20,4 kN
71. 16 N
72. (3 N) î – (11 N) ĵ (4 N) k̂
73. (a) 2,6 N; (b) 17°
74. 2,2 kg
75. (a) 0; (b) 0,83 m/s2; (c) 0
76. (b) F/(m  M); (c) FM/(m  M); (d) F(m  2M)/2(m
 M)
77. (a) 0,74 m/s2; (b) 7,3 m/s2
78. 4,6 N
79. (a) 11 N; (b) 2,2 kg; (c) 0; (d) 2,2 kg
80. (a) 620 N; (b) 580 N
81. 195 N
82. (a) (1,0 î − 1,3 ĵ) m/s2; (b) 1,6 m/s2; (c) –50°
83. (a) 4,6 m/s2; (b) 2,6 m/s2
84. (a) cos ; (b) (cos )0,5
85. (a) a corda arrebenta; (b) 1,6 m/s2
86. (a) 7,4  102 N; (b) 2,8  102 N; (c) 0; (d) 75 kg
87. (a) 65 N; (b) 49 N
88. (a) 3260 N; (b) 2,7  103 kg; (c) 1,2 m/s2
89. (a) 4,6  103 N; (b) 5,8  103 N
90. (a) 1,2  102 m/s2; (b) 12g; (c) 1,4  108 N; (d) 4,2 anos
91. (a) 1,8  102 N; (b) 6,4  102 N
92. 10 m/s2
93. (a) 44 N; (b) 78 N; (c) 54 N; (d) 152 N
94. (a) (5,0 m/s) î  (4,3 m/s) ĵ; (b) (15 m) î  (6,4 m) ĵ
95. (a) 4 kg; (b) 6,5 m/s2; (c) 13 N
96. 16 N
Capítulo 6
1. 36 m
2. 0,58
6
RESPOSTAS DOS PROBLEMAS
3. (a) 2,0  102 N; (b) 1,2  102 N
4. 0,53
5. (a) 6,0 N; (b) 3,6 N; (c) 3,1 N
6. 0,61
7. (a) 1,9  102 N; (b) 0,56 m/s2
8. 1,6  102 N
9. (a) 11 N; (b) 0,14 m/s2
10. (a) 0; (b) 2,17 m/s2
11. (a) 3,0  102 N; (b) 1,3 m/s2
12. 2,8  102 N
13. (a) 1,3  102 N; (b) não; (c) 1,1  102 N; (d) 46 N;
(e) 17 N
14. (b) 3,0  107 N
15. 2°
16. (a) 8,6 N; (b) 46 N; (c) 39 N
17. (a) (17 N) î; (b) (20 N) î; (c) (15 N) î
18. (a) 12,1 m/s; (b) 19,4 m/s
19. (a) não; (b) (−12 N) î  (5,0 N) ĵ
20. 8,5 N
21. (a) 19°; (b) 3,3 kN
22. 18º
23. 0,37
24. 0,54
25. 1,0  102 N
26. (a) 147 N; (b) igual
27. (a) 0; (b) (−3,9 m/s2) î; (c) (−1,0 m/s2) î
28. 3,3 kg
29. (a) 66 N; (b) 2,3 m/s2
30. (a) 74 N; (b) (76 N)/(cos   0,42 sen ); (c) 23°;
(d) 70 N
31. (a) 3,5 m/s2; (b) 0,21 N
32. 60º
33. 9,9 s
34. (a) (–6,1 m/s2) î; (b) (−0,98 m/s2) î
35. 4,9  102 N
36. 3,75
37. (a) 3,2  102 km/h; (b) 6,5  102 km/h; (c) não
38. (a) 2  104 N; (b) 18g
39. 2,3
40. (a) 66,0 m/s; (b) −2,20  102 dC
41. 0,60
42. 48 km/h
43. 21 m
44. 9,7g
45. (a) mais leve; (b) 778 N; (c) 223 N; (d) 1,11 kN
46. (a) 547 N; (b) 9,53°
47. (a) 10 s; (b) 4,9  102 N; (c) 1,1  103 N
48. (a) 3,7 kN; (b) para cima; (c) 1,3 kN; (d) para baixo
49. 1,37  103 N
50. (a) 4,03  102 N·s/m; (b) −1,50  103 N/s
51. 2,2 km
52. (a) 3,7 kN; (b) para cima; (c) 2,3 kN; (d) para baixo
53. 12°
54. (a) −(mv2/r2) dr; (b) (2mv/r) dv; (c) −(mv3/r2) dT
55. 2,6  103 N
56. 0,078
57. 1,81 m/s
58. (a) 8,0  103 N; (b) 6,9  103 N; (c) 20 m/s; (d) 1,6 
104 N; (e) não
59. (a) 8,74 N; (b) 37,9 N; (c) 6,45 m/s; (d) na direção da
haste
60. (a) 1,05 N; (b) 3,62 m/s2; (c) as respostas seriam
as mesmas, mas a haste estaria comprimida em vez de
tracionada
61. (a) 27 N; (b) 3,0 m/s2
62. 118 N
63. (b) 240 N; (c) 0,60
64. (a) 69 km/h; (b) 139 km/h; (c) sim
65. (a) 210 N; (b) 44,0 m/s
66. 8,8 N
67. g(sen  – 20,5k cos )
68. (a) vmáx  [Rg(tan   s)/(1 – s tan )]0,5; (c) 149 km/h;
(d) 76,2 km/h
69. 3,4 m/s2
70. (a) 0,40 N; (b) 1,9 s
71. (a) 35,3 N; (b) 39,7 N; (c) 320 N
72. 0,74
73. (a) 7,5 m/s2; (b) para baixo; (c) 9,5 m/s2; (d) para baixo
74. (a) 0,13 N; (b) 0,12
75. (a) 3,0  105 N; (b) 1,2°
76. 20°
77. 147 m/s
78. (a) 0,58; (b) 0,54
79. (a) 13 N; (b) 1,6 m/s2
80. 6,2 kN
81. (a) 275 N; (b) 877 N
82. 178 km/h
83. (a) 84,2 N; (b) 52,8 N; (c) 1,87 m/s2
84. (b) 55°; (c) aumenta; (d) 59°
85. 3,4%
86. (a) no ponto mais baixo; (b) 8,73 m/s
87. (a) 3,21  103 N; (b) 3,75  103 N
88. 9,4 N
89. (a) 222 N; (b) 334 N; (c) 311 N; (d) 311 N; (e) c, d
90. (a) 12 N; (b) 10 N; (c) 26 N; (d) 23 N; (e) 32 N; (f) 23
N; (g) d; (h) f; (i) a, c, d
91. (a) v20/(4g sen ); (b) não
92. (a) 11°; (b) 0,19
93. (a) 0,34; (b) 0,24
94. (a) 0,37; (b) 0,37 < s < 0,47
95. (a) kmg/(sen  – k cos ); (b) 0  tan–1 s
96. (a) 0,96 m/s; (b) 0,021
97. 0,18
98. (a) 2,1 m/s2; (b) para baixo; (c) 3,9 m; (d) permanece
em repouso
Capítulo 7
1. (a) 2,9  107 m/s; (b) 2,1  10–13 J
2. 1,8  1013 J
3. (a) 5  1014 J; (b) 0,1 megaton de TNT; (c) 8 bombas
RESPOSTAS DOS PROBLEMAS
4. 7,1 J
5. (a) 2,4 m/s; (b) 4,8 m/s
6. (a) 11 J; (b) –21 J
7. 0,96 J
8. 5,0 kJ
9. 20 J
10. 6,8 J
11. (a) 62,3°; (b) 118°
12. (a) 3,00 N; (b) 9,00 J
13. (a) 1,7  102 N; (b) 3,4  102 m; (c) −5,8  104 J;
(d) 3,4  102 N; (e) 1,7  102 m; (f) −5,8  104 J
14. 15,3 J
15. (a) 1,50 J; (b) aumenta
16. 3,5 m/s
17. (a) 12 kJ; (b) −11 kJ; (c) 1,1 kJ; (d) 5,4 m/s
18. (a) 36 kJ; (b) 2,0  102 J
19. 25 J
20. 45 N
21. (a) −3Mgd/4; (b) Mgd; (c) Mgd/4; (d) (gd/2)0,5
22. (a) 8,84 kJ; (b) 7,84 kJ; (c) 6,84 kJ
23. 4,41 J
24. (a) 1,31 J; (b) 0,935 m/s
25. (a) 25,9 kJ; (b) 2,45 N
26. x  −4,9 cm e x  4,9 cm
27. (a) 7,2 J; (b) 7,2 J; (c) 0; (d) –25 J
28. 1,25 kJ
29. (a) 0,90 J; (b) 2,1 J; (c) 0
30. (a) 8,0 N; (b) 8,0 N/m
31. (a) 6,6 m/s; (b) 4,7 m
32. (a) 16 J; (b) 16 J; (c) 0; (d) –14 J
33. (a) 0,12 m; (b) 0,36 J; (c) –0,36 J; (d) 0,060 m; (e)
0,090 J
34. 8,0  102 J
35. (a) 0; (b) 0
36. 25 J
37. (a) 42 J; (b) 30 J; (c) 12 J; (d) 6,5 m/s, eixo x;
(e) 5,5 m/s, eixo x; (f) 3,5 m/s, eixo x
38. (a) 2,3 J; (b) 2,6 J
39. 4,00 N/m
40. 0,21 J
41. 5,3  102 J
42. 41,7 J
43. (a) 0,83 J; (b) 2,5 J; (c) 4,2 J; (d) 5,0 W
44. (a) 9,0  102 J; (b) 1,1  102 W; (c) 2,3  102 W
45. 4,9  102 W
46. 2,7  105 W
47. (a) 1,0  102 J; (b) 8,4 W
48. (a) 0; (b) –3,5  102 W
49. 7,4  102 W
50. (a) 28 W; (b) (6 m/s) ĵ
51. (a) 32,0 J; (b) 8,00 W; (c) 78,2°
52. (−T/3P) dP
53. (a) 1,20 J; (b) 1,10 m/s
54. (a) 12 J; (b) 4,0 m; (c) 18 J
55. (a) 1,8  105 ft.lb; (b) 0,55 hp
7
56. (a) 1,0  102 J; (b) 67 W; (c) 33 W
57. (a) 797 N; (b) 0; (c) –1,55 kJ; (d) 0; (e) 1,55 kJ; (f) F
varia durante o deslocamento
58. (a) 590 J; (b) 0; (c) 0; (d) 590 J
59. (a) 1  105 megatons de TNT; (b) 1  107 bombas
60. (a) 2,1  102 J; (b) 2,1  102 J
61. −6 J
62. (a) 0,29 J; (b) −1,8 J; (c) 3,5 m/s; (d) 23 cm
63. (a) 98 N; (b) 4,0 cm; (c) 3,9 J; (d) −3,9 J
64. (a) 1,7 W; (b) 0; (c) −1,7 W
65. (a) 314 J; (b) –155 J; (c) 0; (d) 158 J
66. 6,67  105 J
67. (a) 23 mm; (b) 45 N
68. 1,5 kJ
69. 165 kW
70. (a) 6,0 N; (b) −2,5 N; (c) 15 N
71. −37 J
72. (a) vf  (cos )0,5, com vf em metros por segundo;
(b) vf  (1  cos )0,5; (c) vf  (1 − cos )0,5
73. (a) 13 J; (b) 13 J
74. (a) c  4 m; (b) c < 4 m; (c) c > 4 m
75. 235 kW
76. (a) 2,7  102 N; (b) –4,0  102 J; (c) 4,0  102 J; (d) 0;
(e) 0
77. (a) 6 J; (b) 6,0 J
78. (b) x  3,00 m; (c) 13,5 J; (d) x  4,50 m; (e) x  4,50 m
79. (a) 0,6 J; (b) 0; (c) –0,6 J
80. 0,47 J
Capítulo 8
1. 89 N/cm
2. (a) 0; (b) 170 kJ; (c) 340 kJ; (d) 170 kJ; (e) 340 kJ;
(f) aumenta
3. (a) 167 J; (b) −167 J; (c) 196 J; (d) 29 J; (e) 167 J;
(f) −167 J; (g) 296 J; (h) 129 J
4. (a) 1,51 J; (b) –1,51 J; (c) 0; (d) –1,51 J; (e) 1,51 J; (f) 0;
(g) a mesma
5. (a) 4,31 mJ; (b) −4,31 mJ; (c) 4,31 mJ; (d) −4,31 mJ; (e)
todos aumentariam
6. (a) 0,15 J; (b) 0,11 J; (c) 0,19 J; (d) 38 mJ; (e) 75 mJ; (f)
permanecem as mesmas
7. (a) 13,1 J; (b) –13,1 J; (c) 13,1 J; (d) todos aumentam
8. (a) 184 J; (b) –184 J; (c) −184 J
9. (a) 17,0 m/s; (b) 26,5 m/s; (c) 33,4 m/s; (d) 56,7 m; (e)
continuariam as mesmas
10. (a) 12,9 m/s; (b) 12,9 m/s; (c) aumentaria
11. (a) 2,08 m/s; (b) 2,08 m/s; (c) aumentaria
12. (a) 21,0 m/s; (b) 21,0 m/s; (c) 21,0 m/s
13. (a) 0,98 J; (b) –0,98 J; (c) 3,1 N/cm
14. (a) 2,98 m/s; (b) 4,21 m/s; (c) 2,98 m/s; (d)
permaneceriam as mesmas
15. (a) 2,6  102 m; (b) permanece o mesmo; (c) diminui
16. (a) 7,2 J; (b) −7,2 J; (c) 86 cm; (d) 26 cm
17. (a) 2,5 N; (b) 0,31 N; (c) 30 cm
18. (a) 2,29 m/s; (b) permanece a mesma
8
RESPOSTAS DOS PROBLEMAS
19. (a) 784 N/m; (b) 62,7 J; (c) 62,7 J; (d) 80,0 cm
20. (a) 5,0 m/s; (b) 79°; (c) 64 J
21. (a) 8,35 m/s; (b) 4,33 m/s; (c) 7,45 m/s; (d) diminuem
22. (a) 4,4 m; (b) seria igual
23. (a) 4,85 m/s; (b) 2,42 m/s
24. 10 cm
25. −3,2  102 J
26. (a) U  27  12x – 3x2; (b) 39 J; (c) –1,6 m; (d) 5,6 m
27. (a) não; (b) 9,3  102 N
28. (a) 2,8 m/s; (b) 2,7 m/s
29. (a) 35 cm; (b) 1,7 m/s
30. (a) 0,81 m/s; (b) 0,21 m; (c) 6,3 m/s2; (d) para cima
31. (a) 39,2 J; (b) 39,2 J; (c) 4,00 m
32. 1,0 mJ
33. (a) 2,40 m/s; (b) 4,19 m/s
34. 9,20 m
35. (a) 39,6 cm; (b) 3,64 cm
36. 1,25 cm
37. −18 mJ
38. (a) 8,37 m/s; (b) 12,6 m/s; (c) 7,67 m; (d) 1,73 m
39. (a) 2,1 m/s; (b) 10 N; (c) x; (d) 5,7 m; (e) 30 N; (f) −x
40. (a) 1,12(A/B)1/6; (b) repulsiva; (c) atrativa
41. (a) −3,7 J; (c) 1,3 m; (d) 9,1 m; (e) 2,2 J; (f) 4,0 m;
(g) (4 − x)e–x/4; (h) 4,0 m
42. (a) 5,6  102 J; (b) 5,6  102 J
43. (a) 5,6 J; (b) 3,5 J
44. (a) 105 J; (b) 30,6 J; (c) 34,4 J
45. (a) 30,1 J; (b) 30,1 J; (c) 0,225
46. 20 ft.lb
47. 0,53 J
48. 75 J
49. (a) –2,9 kJ; (b) 3,9  102 J; (c) 2,1  102 N
50. 11 kJ
51. (a) 1,5 MJ; (b) 0,51 MJ; (c) 1,0 MJ; (d) 63 m/s
52. (a) 0,292 m; (b) 14,2 J
53. (a) 67 J; (b) 67 J; (c) 46 cm
54. (a) 1,5  102 J; (b) 5,5 m/s
55. (a) −0,90 J; (b) 0,46 J; (c) 1,0 m/s
56. 0,15
57. 1,2 m
58. (a) 13 cm; (b) 2,7 m/s; (c) aumentam
59. (a) 19,4 m; (b) 19,0 m/s
60. 4,3 m
61. (a) 1,5  10–2 N; (b) (3,8  102)g
62. 3,5 m/s
63. (a) 7,4 m/s; (b) 90 cm; (c) 2,8 m; (d) 15 m
64. H  30 cm
65. 20 cm
66. (a) 94 J; (b) 94 J; (c) 7,7 m/s
67. (a) 7,0 J; (b) 22 J
68. (a) 54 m/s; (b) 52 m/s; (c) −76 m
69. 3,7 J
70. 0,72 m
71. 4,33 m/s
72. (a) 44 m/s; (b) 0,036
73. 25 J
74. (a) 6,4 m/s; (b) 4,9 m/s; (c) iguais
75. (a) 4,9 m/s; (b) 4,5 N; (c) 71°; (d) permanece a mesma
76. (a) 18 J; (b) 0; (c) 30 J; (d) 0; (e) b e d
77. (a) 4,8 N; (b) x; (c) 1,5 m; (d) 13,5 m; (e) 3,5 m/s
78. (a) 216 J; (b) 1,18 kN; (c) 432 J; (d) o motor também
fornece energia térmica ao caixote e à esteira
79. (a) 24 kJ; (b) 4,7  102 N
80. 17 kW
81. (a) 5,00 J; (b) 9,00 J; (c) 11,0 J; (d) 3,00 J; (e) 12,0 J;
(f) 2,00 J; (g) 13,0 J; (h) 1,00 J; (i) 13,0 J; (j) 1,00 J; (l)
11,0 J; (m) 10,8 m; (n) volta para x  0 e para.
82. (a) 0,950 m/s; (b) 11,0 m
83. (a) 6,0 kJ; (b) 6,0  102 W; (c) 3,0  102 W; (d) 9,0 
102 W
84. (a) 31,0 J; (b) 5,35 m/s; (c) conservativa
85. 880 MW
86. (a) 13 m/s; (b) 11 m/s; (c) não, 9,3 m
87. (a) v0  (2gL)0,5; (b) 5mg; (c) –mgL; (d) –2mgL
88. (a) 6,75 J; (b) –6,75 J; (c) 6,75 J; (d) 6,75 J; (e) –6,75 J;
(f) 0,459 m
89. (a) 109 J; (b) 60,3 J; (c) 68,2 J; (d) 41,0 J
90. (a) 2,2 kJ; (b) 7,7  102 J
91. (a) 2,7 J; (b) 1,8 J; (c) 0,39 m
92. 56 m/s
93. (a) 10 m; (b) 49 N; (c) 4,1 m; (d) 1,2  102 N
94. 5,5  106 N
95. (a) 5,5 m/s; (b) 5,4 m; (c) permanecem as mesmas
96. (a) 3,5 kJ; (b) 3,5 kJ
97. 80 mJ
98. 181 W
99. 24 W
100. 100 m
101. −12 J
102. (a) 7,8 MJ; (b) 6,2 bars
103. (a) 8,8 m/s; (b) 2,6 kJ; (c) 1,6 kW
104. (a) 19 J; (b) 6,4 m/s; (c) 11 J, 6,4 m/s
105. (a) 7,4  102 J; (b) 2,4  102 J
106. (a) 12 m/s; (b) 11 cm
107. 15 J
108. (a) Entre 0,2 e 0,3 MJ; (b) a mesma
109. (a) 2,35  103 J; (b) 352 J
110. (a) 2,6 m; (b) 1,5 m; (c) 26 J; (d) 2,1 m/s
111. 738 m
112. 8580 J
113. (a) –3,8 kJ; (b) 31 kN
114. (a) 3,0  105 J; (b) 10 kW; (c) 20 kW
115. (a) 300 J; (b) 93,8 J; (c) 6,38 m
116. (a) 39 kW; (b) 39 kW
117. (a) 5,6 J; (b) 12 J; (c) 13 J
118. 69 hp
119. (a) 1,2 J; (b) 11 m/s; (c) não; (d) não
120. (a) –0,80 J; (b) –0,80 J; (c) 1,1 J
121. (a) 2,1  106 kg; (b) (100  1,5t)0,5 m/s; (c) (1,5 
106)/(100  1,5t)0,5 N; (d) 6,7 km
122. (a) 3,7 J; (b) 4,3 J; (c) 4,3 J
RESPOSTAS DOS PROBLEMAS
Capítulo 9
1. (a) −1,50 m; (b) −1,43 m
2. (a) 1,1 m; (b) 1,3 m; (c) se aproxima
3. (a) −6,5 cm; (b) 8,3 cm; (c) 1,4 cm
4. (a) 11 cm; (b) −4,4 cm
5. (a) –0,45 cm; (b) –2,0 cm
6. (a) 20 cm; (b) 20 cm; (c) 16 cm
7. (a) 0; (b) 3,13  1011 m
8. (a) 6,0 cm; (b) 6,0 cm; (c) desce até um certo ponto e
depois sobe até 6,0 cm; (d) 4,2 cm
9. (a) 28 cm; (b) 2,3 m/s
10. (a) 22 m; (b) 9,3 m/s
11. (−4,0 m) î  (4,0 m) ĵ
12. 6,2 m
13. 53 m
14. (a) 5,74 m; (b) (10,0 m/s) î; (c) (−3,68 m/s2) ĵ
15. (a) (2,35 î − 1,57 ĵ) m/s2; (b) (2,35 î – 1,57 ĵ)t m/s, com
t em segundos; (d) retilínea, fazendo um ângulo de 34° para
baixo
16. 58 kg
17. 4,2 m
18. 4,9 kg·m/s
19. (a) 7,5  104 J; (b) 3,8  104 kg·m/s; (c) 39° ao sul do
leste
20. 48°
21. (a) 5,0 kg·m/s; (b) 10 kg·m/s
22. (a) 30,0°; (b) (−0,572 kg·m/s) ĵ
23. 1,0  103 a 1,2  103 kg·m/s
24. (a) 1,1 m; (b) 4,8  103 kg·m/s
25. (a) 42 N.s; (b) 2,1 kN
26. (a) 2,2  102 N·s; (b) 2,7  103 N
27. (a) 67 m/s; (b) −x; (c) 1,2 kN; (d) –x
28. (a) 9,1 N·s; (b) 1,8  103 N
29. 5 N
30. (a) 1,00 N·s; (b) 100 N; (c) 20 N
31. (a) 2,39  103 N·s; (b) 4,78  105 N; (c) 1,76  103 N·s;
(d) 3,52  105 N
32. (a) (30 kg·m/s) î; (b) (38 kg·m/s) î; (c) (6,0 m/s) î
33. (a) 5,86 kg·m/s; (b) 59,8°; (c) 2,93 kN; (d) 59,8°
34. (a) 4,50  10–3 N·s; (b) 0,529 N·s; (c) afundar
35. 9,9  102 N
36. (a) 7,17 N·s; (b) 16,0 kg·m/s
37. (a) 9,0 kg·m/s; (b) 3,0 kN; (c) 4,5 kN; (d) 20 m/s
38. (a) (1,8 N·s) ĵ; (b) (−180 N) ĵ
39. 3,0 mm/s
40. 4,4  103 km/h
41. (a) –(0,15 m/s) î; (b) 0,18 m
42. mv2/6
43. 55 cm
44. 3,4 kg
45. (a) (1,00 î – 0,167 ĵ) km/s; (b) 3,23 MJ
46. 3,5 m/s
47. (a) 14 m/s; (b) 45°
48. (a) 20 J; (b) 40 J
49. 3,1  102 m/s
9
50. (a) 1,81 m/s; (b) 4,96 m/s
51. (a) 721 m/s; (b) 937 m/s
52. 7,3 cm
53. (a) 33%; (b) 23%; (c) diminui
54. 2,6 m
55. (a) 2,0 m/s; (b) −1,3 J; (c) 40 J; (d) o sistema
recebeu energia de alguma fonte, como, por exemplo, uma
pequena explosão
56. (a) 4,6 m/s; (b) 3,9 m/s; (c) 7,5 m/s
57. (a) 4,4 m/s; (b) 0,80
58. 33 cm
59. 25 cm
60. (a) 1,9 m/s; (b) para a direita; (c) sim
61. (a) 99 g; (b) 1,9 m/s; (c) 0,93 m/s
62. (a) 100 g; (b) 1,0 m/s
63. (a) 3,00 m/s; (b) 6,00 m/s
64. (a) 2,47 m/s; (b) 1,23 m/s
65. (a) 1,2 kg; (b) 2,5 m/s
66. (a) 30 cm; (b) 3,3 m
67. –28 cm
68. (a) 2,22 m; (b) 0,556 m
69. (a) 0,21 kg; (b) 7,2 m
70. 1,0 kg
71. (a) 4,15  105 m/s; (b) 4,84  105 m/s
72. (a) 27°
73. 120°
74. (a) (10 m/s) î  (15 m/s) ĵ; (b) −500 J
75. (a) 433 m/s; (b) 250 m/s
76. 108 m/s
77. (a) 46 N; (b) nenhuma
78. (a) 2,7; (b) 7,4
79. (a) 1,57  106 N; (b) 1,35  105 kg; (c) 2,08 km/s
80. (a) (−4,0  104 kg.m/s) î; (b) oeste; (c) 0
81. (a) 7290 m/s; (b) 8200 m/s; (c) 1,271  1010 J; (d)
1,275  1010 J
82. 6,0  102
83. (a) 1,92 m; (b) 0,640 m
84. (a) as partículas se movem juntas ao longo do eixo x;
(b) uma das partículas se move ao longo da reta 2 e a outra
ao longo da reta 3; (c) uma das partículas se move na região
B e a outra na região C em trajetórias simétricas em relação
ao eixo x; (d) 3,06 m/s; (e) 4,00 m/s cada partícula
85. (a) 1,78 m/s; (b) menor; (c) menor; (d) maior
86. (a) 7,11 m/s; (b) maior; (c) menor; (d) menor
87. (a) 3,7 m/s; (b) 1,3 N.s; (c) 1,8  102 N
88. 41,7 cm/s
89. (a) (7,4  103 N·s) î − (7,4  103 N·s) ĵ; (b) (−7,4 
103 N·s) î; (c) 2,3  103 N; (d) 2,1  104 N; (e) –45°
90. (a) 1,4  10–22 kg·m/s; (b) 28°; (c) 1,6  10–19 J
91. 4,4 m/s
92. 0,57 m/s
93. 1,18  104 kg
94. 72 km/h
95. (a) 1,9 m/s; (b) −30°; (c) elástica
96. (a) 8,0  104 N; (b) 27 kg/s
10
RESPOSTAS DOS PROBLEMAS
97. (a) 6,9 m/s; (b) 30°; (c) 6,9 m/s; (d) −30°; (e) 2,0 m/s;
(f) –180°
98. (a) (−0,450 î− 0,450 ĵ− 1,08 k̂) kg·m/s; (b) (−0,450 î −
0,450 ĵ− 1,08 k̂) N·s; (c) (0,450 î  0,450 ĵ 1,08 k̂) N·s
99. (a) 25 mm; (b) 26 mm; (c) para baixo; (d) 1,6  10–2 m/s2
100. (a) 41,0°; (b) 4,75 m/s; (c) não
101. 29 J
102. (a) para baixo; (b) 0,50 m/s; (c) 0
103. 2,2 kg
104. 3,0 m
105. 5,0 kg
106. (a) 0,54 m/s; (b) 0; (c) 1,1 m/s
107. (a) 50 kg/s; (b) 1,6  102 kg/s
108. 2,5  103
109. (a) 4,6  103 km; (b) 73%
110. (a) 2,18 kg.m/s; (b) 575 N
111. 190 m/s
112. (a) 1,0 kg·m/s; (b) 2,5  102 J; (c) 10 N; (d) 1,7 kN;
(e) porque a resposta do item (c) inclui o tempo entre
colisões
113. 28,8 N
114. (a) −0,25 m; (b) 0
115. (a) 0,745 mm; (b) 153°; (c) 1,67 mJ
116. (a) 0; (b) 0,75 m
117. (a) (2,67 m/s) î  (−3,00 m/s) ĵ; (b) 4,01 m/s; (c) 48,4°
118. (a) 0,60 cm; (b) 4,9 cm; (c) 9,0 cm; (d) 0
119. (a) –0,50 m; (b) –1,8 cm; (c) 0,50 m
120. (a) 0; (b) 4,0 m/s
121. 0,22%
122. 1,10 m/s
Capítulo 10
1. 14 rev
2. (a) 0,105 rad/s; (b) 1,75  10–3 rad/s; (c) 1,45  10–4 rad/s
3. (a) 4,0 rad/s; (b) 11,9 rad/s
4. (a) 2,0 rad; (b) 0; (c) 1,3  102 rad/s; (d) 32 rad/s2; (e) não
5. 11 rad/s
6. (a) 4,0 rad/s; (b) 28 rad/s; (c) 12 rad/s2; (d) 6,0 rad/s2;
(e) 18 rad/s2
7. (a) 1,2t5 – 1,3t3  2,0; (b) 0,20t6 – 0,33t4  2,0t  1,0
8. (a) 1,2t5 – 1,3t3  2,0; (b) 0,20t6 – 0,33t4  2,0t  1,0
9. (a) 3,00 s; (b) 18,9 rad
10. (a) 2,0 rad/s2; (b) 5,0 rad/s; (c) 10 rad/s; (d) 75 rad
11. (a) 30 s; (b) 1,8  103 rad
12. (a) 9,0  103 rev/min2; (b) 4,2  102 rev
13. (a) 3,4  102 s; (b) –4,5  10–3 rad/s2; (c) 98 s
14. (a) 1,0 rev/s2; (b) 4,8 s; (c) 9,6 s; (d) 48 rev
15. 8,0 s
16. (a) 4,09 s; (b) 1,70 s
17. (a) 44 rad; (b) 5,5 s; (c) 32 s; (d) −2,1 s; (e) 40 s
18. (a) 3,1  102 m/s; (b) 3,4  102 m/s
19. (a) 2,50  10–3 rad/s; (b) 20,2 m/s2; (c) 0
20. (a) 6,4 cm/s2; (b) 2,6 cm/s2
21. 6,9  1013 rad/s
22. (a) 3,0 rad/s; (b) 30 m/s; (c) 6,0 m/s2; (d) 90 m/s2
23. (a) 20,9 rad/s; (b) 12,5 m/s; (c) 800 rev/min2; (d) 600 rev
24. 199 toques/s
25. (a) 7,3  10–5 rad/s; (b) 3,5  102 m/s; (c) 7,3  10–5
rad/s; (d) 4,6  102 m/s
26. (a) −1,1 rev/min2; (b) 9,9  103 rev; (c) −0,99 mm/s2;
(d) 31 m/s2
27. (a) 73 cm/s2; (b) 0,075; (c) 0,11
28. 16 s
29. (a) 3,8  103 rad/s; (b) 1,9  102 m/s
30. (a) 40,2 cm/s2; (b) 2,36  103 m/s2; (c) 83,2 m
31. (a) 40 s; (b) 2,0 rad/s2
32. (a) −2,3  10–9 rad/s2; (b) 2,6  103 anos; (c) 24 ms
33. 12,3 kg·m2
34. (a) 1,5 rad/s2; (b) 0,40 J
35. (a) 1,1 kJ; (b) 9,7 kJ
36. 2,5 kg
37. 0,097 kg·m2
38. (a) 7,1%; (b) 64%
39. (a) 49 MJ; (b) 1,0  102 min
40. (a) 8,352  10–3 kg·m2; (b) −0,22%
41. (a) 0,023 kg·m2; (b) 11 mJ
42. (a) 1,3  103 g·cm2; (b) 5,5  102 g·cm2; (c) 1,9  103
g·cm2; (d) A  B
43. 4,7  10–4 kg·m2
44. (a) 2,0 kg·m2; (b) 6,0 kg·m2; (c) 2,0 kg·m2
45. −3,85 N·m
46. 12 N·m
47. 4,6 N·m
48. (a) 8,4 N·m; (b) 17 N·m; (c) 0
49. (a) 28,2 rad/s2; (b) 338 N·m
50. 1,28 kg·m2
51. (a) 6,00 cm/s2; (b) 4,87 N; (c) 4,54 N; (d) 1,20 rad/s2;
(e) 0,0138 kg·m2
52. (a) 9,7 rad/s2; (b) sentido anti-horário
53. 0,140 N
54. (a) 3,0 rad/s2; (b) 9,4 rad/s2
55. 2,51  10–4 kg·m2
56. (a) 1,7 m/s2; (b) 6,9 m/s2
57. (a) 4,2  102 rad/s2; (b) 5,0  102 rad/s
58. (a) 1,4 m/s; (b) 1,4 m/s
59. 396 N·m
60. (a) 0,63 J; (b) 0,15 m
61. (a) −19,8 kJ; (b) 1,32 kW
62. (a) 11,2 mJ; (b) 33,6 mJ; (c) 56,0 mJ; (d) 2,80  10–5
J·s2/rad2
63. 5,42 m/s
64. (a) 0,15 kg·m2; (b) 11 rad/s
65. (a) 5,32 m/s2; (b) 8,43 m/s2; (c) 41,8°
66. 1,4 m/s
67. 9,82 rad/s
68. (a) 0,689 N·m; (b) 3,05 N; (c) 9,84 N·m; (d) 11,5 N
69. 6,16  10–5 kg·m2
70. (a) 27,0 rad/s; (b) 13,5 s
71. (a) 31,4 rad/s2; (b) 0,754 m/s2; (c) 56,1 N; (d) 55,1 N
72. (a) –7,66 rad/s2; (b) –11,7 N·m; (c) 4,59  104 J; (d)
624 rev; (e) 4,59  104 J
RESPOSTAS DOS PROBLEMAS
73. (a) 4,81  105 N; (b) 1,12  104 N·m; (c) 1,25  106 J
74. (a) 8,6 s; (b) não
75. (a) 2,3 rad/s2; (b) 1,4 rad/s2
76. 1,5  103 rad
77. (a) –67 rev/min2; (b) 8,3 rev
78. 6,06 rad/s
79. – – –
80. (a) 5,00 rad/s; (b) 1,67 rad/s2; (c) 2,50 rad
81. 3,1 rad/s
82. 3  105 J
83. (a) 1,57 m/s2; (b) 4,55 N; (c) 4,94 N
84. (a) 5,1 h; (b) 8,1 h
85. 30 rev
86. 146 rad/s
87. 0,054 kg·m2
88. (a) 155 kg·m2; (b) 64,4 kg
89. 1,4  102 N·m
90. (a) –1,25 rad/s2; (b) 250 rad; (c) 39,8 rev
91. (a) 10 J; (b) 0,27 m
92. (a) 5,5  1015 s; (b) 26
93. 4,6 rad/s2
94. (a) 1,94 m/s2; (b) 75,1°
95. 2,6 J
96. 25 N
97. (a) 5,92  104 m/s2; (b) 4,39  104 s–2
98. 1,6 kg·m2
99. (a) 0,791 kg·m2; (b) 1,79  10–2 N·m
100. (a) 0,019 kg·m2; (b) 0,019 kg·m2
101. (a) 1,5  102 cm/s; (b) 15 rad/s; (c) 15 rad/s; (d) 75
cm/s; (e) 3,0 rad/s
102. (a) 3,3 J; (b) 2,9 J
103. (a) 7,0 kg·m2; (b) 7,2 m/s; (c) 71°
104. (a) 0,20 kg·m2; (b) 6,3 rad/s
Capítulo 11
1. (a) 0; (b) (22 m/s) î ; (c) (−22 m/s) î; (d) 0; (e) 1,5  103
m/s2; (f) 1,5  103 m/s2; (g) (22 m/s) î; (h) (44 m/s) î; (i) 0;
(j) 0; (k) 1,5  103 m/s2; (l) 1,5  103 m/s2
2. (a) 59,3 rad/s; (b) 9,31 rad/s2; (c) 70,7 m
3. −3,15 J
4. (a) 8,0°; (b) maior
5. 0,020
6. 7,2  104 kg·m2
7. (a) 63 rad/s; (b) 4,0 m
8. (a) 2,0 m; (b) 7,3 m/s
9. 4,8 m
10. (a) 8,0 J; (b) 3,0 m/s; (c) 6,9 J; (d) 1,8 m/s
11. (a) (−4,0 N) î; (b) 0,60 kg·m2
12. (a) 37,8 cm; (b) 1,96  10–2 N; (c) na direção do centro
da curva
13. 0,50
14. 1,34 m/s
15. (a) –(0,11 m); (b) −2,1 m/s2; (c) −47 rad/s2; (d) 1,2 s;
(e) 8,6 m; (f) 6,1 m/s
16. 0,25
11
17. (a) 13 cm/s2; (b) 4,4 s; (c) 55 cm/s; (d) 18 mJ; (e) 1,4 J;
(f) 27 rev/s
18. (a) 0,19 m/s2; (b) 0,19 m/s2; (c) 1,1 kN; (d) não; (e)
igual; (f) maior
19. (−2,0 N.m) î
20. (a) (24 N·m) ĵ; (b) (−24 N·m) ĵ; (c) (12 N·m) ĵ; (d) (−12
N·m) ĵ
21. (a) (6,0 N·m) ĵ (8,0 N·m) k̂; (b) (−22 N·m) î
22. –5,00 N
23. (a) (−1,5 N·m) î − (4,0 N·m) ĵ − (1,0 N·m) k̂; (b) (−1,5
N·m) î − (4,0 N·m) ĵ − (1,0 N·m) k̂
24. (a) (6,0 N·m) î − (3,0 N·m) ĵ− (6,0 N·m) k̂; (b) (26 N·m)
î  (3,0 N·m) ĵ− (18 N·m) k̂; (c) (32 N·m) î − (24 N·m) k̂;
(d) 0
25. (a) (50 N·m) k̂; (b) 90°
26. (a) 12 kg·m2/s; (b) z; (c) 3,0 N·m; (d) z
27. (a) 0; (b) (8,0 N·m) î  (8,0 N·m) k̂
28. (a) (6,0  102 kg·m2/s) k̂; (b) (7,2  102 kg·m2/s) k̂
29. (a) 9,8 kg·m2/s; (b) A direção z
30. (a) (3,00 m/s2) î − (4,00 m/s2) ĵ  (2,00 m/s2) k̂;
(b) (42,0 kg·m2/s) î  (24,0 kg·m2/s) ĵ (60,0 kg·.m2/s) k̂;
(c) (–8,00 N·m) î − (26,0 N·m) ĵ− (40,0 N·m) k̂; (d) 127°
31. (a) 0; (b) –22,6 kg·m2/s; (c) –7,84 N·m; (d) –7,84 N·m
32. (2,0 N·m) î  (−4,0 N·m) ĵ
33. (a) (−1,7  102 kg·m2/s) k̂; (b) (56 N·m) k̂; (c) (56
kg·m2/s2) k̂
34. (a) 0; (b) (−8,0t k̂) N·m; (c) (–2,0t0,5 k̂) N·m; (d) (8,0t–3
k̂) N·m
35. (a) 48t k̂ N·m; (b) aumentando
36. 1024
37. (a) 4,6  10–3 kg.m2; (b) 1,1  10–3 kg·m2/s; (c) 3,9 
10–3 kg·m2/s
38. (a) 0,53 kg·m2/s; (b) 4,2  103 rev/min
39. (a) 1,47 N·m; (b) 20,4 rad; (c) −29,9 J; (d) 19,9 W
40. 23 kg·m2/s
41. (a) 1,6 kg·m2; (b) 4,0 kg·m2/s
42. (a) 24 kg·m2/s; (b) 1,5 kg·m2/s
43. (a) 1,5 m; (b) 0,93 rad/s; (c) 98 J; (d) 8,4 rad/s; (e) 8,8
 102 J; (f) da energia interna das patinadoras
44. (a) 4,2 rad/s; (b) não, por causa da energia transferida
para a energia interna da barata
45. (a) 3,6 rev/s; (b) 3,0; (c) a força que o homem exerce
sobre os tijolos converte energia interna do homem em
energia cinética
46. 3
47. 0,17 rad/s
48. 0,20
49. (a) 750 rev/min; (b) 450 rev/min; (c) horário
50. 5,0  102 rev
51. (a) 267 rev/min; (b) 0,667
52. (a) 0,347 rad/s; (b) 1,33; (c) por causa da energia
transferida da energia interna da barata para energia
cinética
53. 1,3  103 m/s
54. 39,1 J
12
RESPOSTAS DOS PROBLEMAS
55. 3,4 rad/s
56. 6,46 kg·m2/s
57. (a) 18 rad/s; (b) 0,92
58. 2,6 rad/s
59. 11,0 m/s
60. (a) 0,24 kg·m2; (b) 1,8  103 m/s
61. 1,5 rad/s
62. 3,23 rev/s
63. 0,070 rad/s
64. 1,5
65. (a) 0,148 rad/s; (b) 0,0123; (c) 181°
66. 32°
67. (a) 0,180 m; (b) horário
68. (a) 0,33 rev/s; (b) horário
69. 0,041 rad/s
70. 2,33 m/s
71. (a) 1,6 m/s2; (b) 16 rad/s2; (c) (4,0 N) î
72. 1,00
73. (a) 0; (b) 0; (c) –30t3 k̂ kg·m2/s; (d) –90t2 k̂, N·m; (e)
30t3 k̂, kg·m2/s; (f) 90t2 k̂, N·m
74. 12 s
75. (a) 149 kg·m2; (b) 158 kg·m2/s; (c) 0,744 rad/s
76. 0,62 J
77. (a) 6,65  10–5 kg·m2/s; (b) não; (c) 0; (d) sim
78. (a) 4,11 m/s2; (b) 16,4 rad/s2; (c) 2,55 N·m
79. (a) 0,333; (b) 0,111
80. (5,55 kg·m2/s) k̂
81. (a) 58,8 J; (b) 39,2 J
82. (a) 12,2 kg·m2; (b) 308 kg·m2/s
83. (a) 61,7 J; (b) 3,43 m; (c) não
84. (a) 0,89 s; (b) 9,4 J; (c) 1,4 m/s; (d) 0,12 J; (e) 4,4 
102 rad/s; (f) 9,2 J
85. (a) mvR/(I  MR2); (b) mvR2/(I  MR2)
86. (a) (–24t2 kg·m2/s) k̂; (b) (–48t N·m) k̂; (c) (12t2 kg·m2/s)
k̂; (d) (24t N·m) k̂
87. a velocidade de rotação ficaria menor; o dia ficaria
cerca de 0,8 s mais longo
88. 1,2  108 kg·m2/s
89. (a) 12,7 rad/s; (b) horário
90. 2,5  1011 kg·m2/s
91. (a) 0,81 mJ; (b) 0,29; (c) 1,3  10–2 N
92. (a) 9,9  102 J; (b) 3,0  103 J; (c) 1,2  105 J
93. (a) mR2/2; (b) um cilindro circular